Max Guercy led Rice (7-16, 2-8) with 17 points. Austin Ramljak was next with 11 points. Sean Obi was one point short of a double-double with nine points and 12 rebounds.
Tulsa shot 43 percent (22-of-51) from the floor, hit just two treys out of 11 attempts and connected 65 percent (20-of-31) from the foul line.
Rice finished with 37 percent (18-of-49) shooting, 25 percent (7-of-25) in 3s and 65 percent (13-of-20) from the free throw line.
TU returns home to meet East Carolina Thursday night at the Reynolds Center. Game time is at 7 p.m.